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  <div class="section" id="numpy-fft-fftn">
<h1>numpy.fft.fftn<a class="headerlink" href="#numpy-fft-fftn" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.fft.fftn">
<code class="sig-prename descclassname">numpy.fft.</code><code class="sig-name descname">fftn</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">s=None</em>, <em class="sig-param">axes=None</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/fft/_pocketfft.py#L663-L758"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.fft.fftn" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the N-dimensional discrete Fourier Transform.</p>
<p>This function computes the <em>N</em>-dimensional discrete Fourier Transform over
any number of axes in an <em>M</em>-dimensional array by means of the Fast Fourier
Transform (FFT).</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>a</strong><span class="classifier">array_like</span></dt><dd><p>Input array, can be complex.</p>
</dd>
<dt><strong>s</strong><span class="classifier">sequence of ints, optional</span></dt><dd><p>Shape (length of each transformed axis) of the output
(<code class="docutils literal notranslate"><span class="pre">s[0]</span></code> refers to axis 0, <code class="docutils literal notranslate"><span class="pre">s[1]</span></code> to axis 1, etc.).
This corresponds to <code class="docutils literal notranslate"><span class="pre">n</span></code> for <code class="docutils literal notranslate"><span class="pre">fft(x,</span> <span class="pre">n)</span></code>.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped.  If it is larger, the input is padded with zeros.
if <em class="xref py py-obj">s</em> is not given, the shape of the input along the axes specified
by <em class="xref py py-obj">axes</em> is used.</p>
</dd>
<dt><strong>axes</strong><span class="classifier">sequence of ints, optional</span></dt><dd><p>Axes over which to compute the FFT.  If not given, the last <code class="docutils literal notranslate"><span class="pre">len(s)</span></code>
axes are used, or all axes if <em class="xref py py-obj">s</em> is also not specified.
Repeated indices in <em class="xref py py-obj">axes</em> means that the transform over that axis is
performed multiple times.</p>
</dd>
<dt><strong>norm</strong><span class="classifier">{None, “ortho”}, optional</span></dt><dd><div class="versionadded">
<p><span class="versionmodified added">New in version 1.10.0.</span></p>
</div>
<p>Normalization mode (see <a class="reference internal" href="../routines.fft.html#module-numpy.fft" title="numpy.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.fft</span></code></a>). Default is None.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">complex ndarray</span></dt><dd><p>The truncated or zero-padded input, transformed along the axes
indicated by <em class="xref py py-obj">axes</em>, or by a combination of <em class="xref py py-obj">s</em> and <em class="xref py py-obj">a</em>,
as explained in the parameters section above.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>ValueError</strong></dt><dd><p>If <em class="xref py py-obj">s</em> and <em class="xref py py-obj">axes</em> have different length.</p>
</dd>
<dt><strong>IndexError</strong></dt><dd><p>If an element of <em class="xref py py-obj">axes</em> is larger than than the number of axes of <em class="xref py py-obj">a</em>.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="../routines.fft.html#module-numpy.fft" title="numpy.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.fft</span></code></a></dt><dd><p>Overall view of discrete Fourier transforms, with definitions and conventions used.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.ifftn.html#numpy.fft.ifftn" title="numpy.fft.ifftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifftn</span></code></a></dt><dd><p>The inverse of <a class="reference internal" href="#numpy.fft.fftn" title="numpy.fft.fftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fftn</span></code></a>, the inverse <em>n</em>-dimensional FFT.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.fft.html#numpy.fft.fft" title="numpy.fft.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft</span></code></a></dt><dd><p>The one-dimensional FFT, with definitions and conventions used.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.rfftn.html#numpy.fft.rfftn" title="numpy.fft.rfftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">rfftn</span></code></a></dt><dd><p>The <em>n</em>-dimensional FFT of real input.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.fft2.html#numpy.fft.fft2" title="numpy.fft.fft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft2</span></code></a></dt><dd><p>The two-dimensional FFT.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.fftshift.html#numpy.fft.fftshift" title="numpy.fft.fftshift"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fftshift</span></code></a></dt><dd><p>Shifts zero-frequency terms to centre of array</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The output, analogously to <a class="reference internal" href="numpy.fft.fft.html#numpy.fft.fft" title="numpy.fft.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft</span></code></a>, contains the term for zero frequency in
the low-order corner of all axes, the positive frequency terms in the
first half of all axes, the term for the Nyquist frequency in the middle
of all axes and the negative frequency terms in the second half of all
axes, in order of decreasingly negative frequency.</p>
<p>See <a class="reference internal" href="../routines.fft.html#module-numpy.fft" title="numpy.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.fft</span></code></a> for details, definitions and conventions used.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="p">:</span><span class="mi">3</span><span class="p">,</span> <span class="p">:</span><span class="mi">3</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftn</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axes</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="go">array([[[ 0.+0.j,   0.+0.j,   0.+0.j], # may vary</span>
<span class="go">        [ 0.+0.j,   0.+0.j,   0.+0.j],</span>
<span class="go">        [ 0.+0.j,   0.+0.j,   0.+0.j]],</span>
<span class="go">       [[ 9.+0.j,   0.+0.j,   0.+0.j],</span>
<span class="go">        [ 0.+0.j,   0.+0.j,   0.+0.j],</span>
<span class="go">        [ 0.+0.j,   0.+0.j,   0.+0.j]],</span>
<span class="go">       [[18.+0.j,   0.+0.j,   0.+0.j],</span>
<span class="go">        [ 0.+0.j,   0.+0.j,   0.+0.j],</span>
<span class="go">        [ 0.+0.j,   0.+0.j,   0.+0.j]]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftn</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">axes</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="go">array([[[ 2.+0.j,  2.+0.j,  2.+0.j], # may vary</span>
<span class="go">        [ 0.+0.j,  0.+0.j,  0.+0.j]],</span>
<span class="go">       [[-2.+0.j, -2.+0.j, -2.+0.j],</span>
<span class="go">        [ 0.+0.j,  0.+0.j,  0.+0.j]]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">200</span><span class="p">)</span> <span class="o">/</span> <span class="mi">12</span><span class="p">,</span>
<span class="gp">... </span>                     <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">200</span><span class="p">)</span> <span class="o">/</span> <span class="mi">34</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">Y</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">FS</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftn</span><span class="p">(</span><span class="n">S</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftshift</span><span class="p">(</span><span class="n">FS</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
<span class="go">&lt;matplotlib.image.AxesImage object at 0x...&gt;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../_images/numpy-fft-fftn-1.png" src="../../_images/numpy-fft-fftn-1.png" />
</div>
</dd></dl>

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